Just days after the One Fund distributed nearly $61 million to victims of the Boston Marathon bombings, the Massachusetts Bar Association called on Attorney General Martha Coakley to intervene, raising “serious concerns” on Wednesday about the way the charitable donations were divided.

Bar association leaders say a system designed to swiftly distribute compensation through a formula based on the length of hospital stays shortchanged some Marathon victims.

Those victims include a 43-year-old family-practice doctor who has reduced his hours and is seeing fewer patients at his Alabama practice because of blast-related hearing loss, and a 39-year-old international development consultant from Jamaica Plain who said her brain injury — possibly permanent — has left her unable to do simple arithmetic.

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The One Fund classified each as outpatients, meaning they received $8,000. Had they stayed overnight in a hospital, they would have been eligible for $125,000 or more if they stayed multiple nights.

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The system devised by One Fund Boston administrator Kenneth R. Feinberg awarded nearly $1.2 million to amputees who lost one limb and $2.2 million to double amputees, those with permanent brain damage, and families of the dead. Twenty-six of 259 who filed claims by the June 15 deadline were rejected.

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Massachusetts Bar leaders — who praised the outpouring for the One Fund and stressed that they were not criticizing Feinberg personally, only his methods — do not want Coakley to recall the distributed money.

Instead, they want to ensure that the aggrieved have a chance to appeal or apply for additional funds from donations still coming in. The fund has received roughly $2 million in the past week.

“There’s a tremendous amount of money being disbursed, and some of it seems to be disbursed not in the most wise manner or fashion,” said Martin W. Healy, chief legal counsel for the bar association, which called on Coakley to examine the One Fund “through her well-established statutory and legal power to regulate public charities.”

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Feinberg, who also administered the September 11th Victim Compensation Fund, the BP oil spill fund, and the Penn State University sex-abuse settlement fund, disagreed with the criticism but seemed unsurprised.

“No good deed goes unpunished,” he said. “Solomon himself wouldn’t get consensus on this.”

He called the Massachusetts Bar Association a “very credible” organization. He adopted the group’s recommendation earlier in the process to allow victims to submit personal statements as well as medical records, providing a way for victims to elaborate on the impact of injuries.

But the association says he ignored those personal statements when disbursing money, and his days-in-a-hospital methodology deliberately avoided criteria such as age, likelihood of long-term pain or complications, and the extent to which an injury affects a victim’s livelihood.

Feinberg acknowledged that might have left a small number upset. “But I must say the goal here, to distribute $60 million in roughly 60 days at no cost to the claimants, with 100 percent of the $60 million going to the victims, requires rough justice,” he said. “We cannot start evaluating individual claims and individual circumstances without slowing down the process, at great cost to evaluate medical records.”

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Paul E. White and others on the Mass. Bar executive board say that is exactly what the One Fund should have done. He called the focus on length of hospital stay “an arbitrary and approximate measure of how severe a person’s injury is.”

“The lines were drawn so inexactly that all detail was taken out of the process,” said White, a partner in the Boston firm Sugarman, Rogers, Barshak & Cohen who organized a 70-lawyer Mass. Bar pro bono effort to assist Marathon victims with One Fund applications and other issues. “In an effort to do rough justice, in some instances what was done was injustice.”

Still, Feinberg and his staff ended their own volunteer involvement when they cut the checks — mailed or direct-deposited Sunday through Tuesday — for the first $60 million.

Mayor Thomas M. Menino and others who oversee the publicly established charity have yet to determine how the additional money coming in will be distributed.

A spokesman for Coakley acknowledged the bar association’s request Wednesday but declined to comment specifically on whether she would advocate for an appeal process for those whose applications were already reviewed by Feinberg.

“Moving forward, we are actively working with The One Fund, the Massachusetts Office for Victim Assistance, and the city of Boston to provide short- and long-term support to survivors and victims’ families,” said Christopher Loh, the spokesman.

A spokeswoman for the mayor expressed approval of Feinberg’s work.

“It would be impossible to ever make everyone feel whole, and it’s a terrible task to have to try, but we appreciate how well Ken and his team worked in getting through this most difficult process,” Dot Joyce said, adding that the One Fund, in ways yet to be determined, “will continue to be a resource and support for those most impacted on that day.”

Two victims have come forward by name — Joanna Leigh of Jamaica Plain and Scott Weisberg of Birmingham, Ala., — while some others and their lawyers are frustrated with the One Fund but reluctant to speak publicly, said Healy, the bar association counsel.

Weisberg, a physician and runner, flew home to Alabama and thought initially that his impaired hearing would improve. But after seeing specialists and undergoing multiple procedures, he learned that the substantial loss in his left ear is permanent and that age-related hearing loss in his right ear will likely be accelerated, lawyer Melina Goldfarb said.

Weisberg anticipates tens of thousands of dollars in out-of-pocket lifetime expenses for hearing aids, doctor visits, and other costs and has temporarily closed his medical practice. “The amount of compensation is not adequate for the type of injury he received,” said Goldfarb, a Birmingham lawyer.

Joanna Leigh
, a spectator, said her first-aid training led her to run toward the first blast, putting her unwittingly close to the second. She sustained a concussion from that blast but no external wounds, and said she helped in the aftermath to tend to bleeding victims.

In the weeks since, she said, she has suffered myriad neurological and psychological issues.

Her application included a letter from a neurosurgeon who has advised the NFL on concussions and wrote that her “very significant” mental deficits may take months or years to improve.

“I would be surprised if her post-injury course is not an extremely long one, and more probably than not may not be ever greeted with complete resolution,” Dr. Robert C. Cantu wrote.

That was not enough to qualify her for the permanent brain injury category, though Leigh said some of the amputees she has met at support groups will be able to return to work sooner than she will.

“The loss of somebody’s limbs is probably the most horrible thing I could ever imagine,” she said, in an emotional interview at the office of her lawyer, Jeffrey S. Stern, also a Sugarman, Rogers partner. “I just don’t know why the loss of my head and the loss of my senses . . . is worth less than somebody else’s loss.”

Correction: Because of incorrect information provided to the Globe, an earlier version of this article referenced a Boston Marathon runner who had been forced to close his Alabama family-medical practice as a result of his blast-related hearing loss. Instead, the doctor has reduced his hours and is seeing fewer patients, but his practice remains open.